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```212                       Screiv-cutting in Lathe.

by machine, and next filed with a smooth file to obliterate the
tool marks. We will indicate the plates by the numbers in
Fig. 2230. First (r) and (2) are scraped and tried by the colour-
patch method, then (2) and (3), and, finally (3) and (i), the cycle
of operation being repeated until all fit together with great
accuracy. The reason for this method is shewn in the diagram.
Thus—(i) and (2) may happen to be convex and concave ; then
(2) and (3) would be made concave and convex. But if (3) and
(i) be now put together, the convexity (or concavity) of both will
be apparent, and may, of course, be corrected. But when all
three fit equally well they must clearly be equally true.

Although fitting processes are less performed now than hereto-
fore, yet all the best work is trued up by the last-described
methods, after it comes off the machine, for however perfect the
latter may be, there is always some little distortion caused by
clamping the work, which, though slight, must be removed if
great.accuracy be required. (See Appendix //,/. 814.)

Cutting a Screw in the Lathe.—This cannot be fully
discussed until velocity ratio of toothed gearing has been entered
on, but the practical considerations may be detailed. It will be
clear, from what has been said in Chapter V., that if the leading
screw be connected to the mandrel in such a way as to revolve at
the same rate, a tool of the shape shewn in Fig. 224 will cut a
screw groove on the spindle that has been centred in the lathe,
of the same pitch as the leading screw thread. If, on the other
hand, the mandrel were to rotate at twice the velocity of the
leading screw, a screw of half the pitch would be formed on the
work, or of twice the number of threads per inch. Summing up
then, the pitch obtained will depend on the relative velocities of
mandrel and leading screw, a proportionately quicker speed of
mandrel giving a finer thread, and a slower speed a coarser thread.
The consideration of the proper change wheels to be introduced
will be left for Part II., but we may here point out that when
both shafts turn in the same direction the screw produced will be
right-handed (viz., same as its leading screw), and when revolving
oppositewise a left-handed screw will "be the result (Seep. 484.)

The correct section of V thread, as adopted by Sir Joseph
Whitworth, is shewn at Fig. 225, one-sbfth of the theoretical```